What is it called when you type math directly into a property?
Despite saying it's not what you want, what you've described is a driver. It might sometimes be called a 'Scripted Expression' (and the Blender Manual now refers to it simply as an 'Expression'), but it's still just a type of driver.
Type #frame * 10 into a property field, e.g. the 'X' location of an object, and press Enter and the property will turn purple, indicating the expression has automatically been turned into a driver. This driver can then be tweaked either by clicking on the property again or by looking in the 'Drivers Editor'.
The types of commands that can be typed into property fields are called 'Simple Expressions'.
An example of the keywords you can type into a property from the Blender Manual:

Globals
frame
Constants
pi, True, False
Operators
+, -, *, /, ==, !=, &lt;, &lt;=, &gt;, &gt;=, and, or, not, conditional operator/ ternary if
Functions
min, max, radians, degrees, abs, fabs, floor, ceil, trunc, int, sin, cos, tan, asin, acos, atan, atan2, exp, log, sqrt, pow, fmod

Note: You need to have a # symbol in front of the expression, e.g. #frame * 2. In the case of 'Constants', 'Operators' and 'Functions' (but not frame), if you omit the # Blender will simply change the property to be the result of the expression, but it won't be driven by it.